This application claims the priority of Japanese Patent Applications No. 61169/1993 filed Feb. 24, 1993 and No. 13145/1994 filed Jan. 10, 1994, which are incorporated herein by reference.
This invention relates to a new method for detecting the phase difference .increment..theta. from a phase-modulated gyroscope. Thus, a phase-modulated gyroscope will be now explained by FIG. 11. A light source 111 emits light beams. The light beams ( waves ) enter an end of a single-mode fiber, pass through a first coupler and attain a polarizer P. The light waves are converted into linearly-polarized waves. The polarized waves are divided into halves by a second coupler. The divided waves are introduced to two ends of a fiber coil 112 of a single-mode fiber wound a plurality of turns around a bobbin. The divided, 5partial waves propagate clockwise and counterclockwise in the fiber coil. No phase difference occurs between the clockwise spreading waves and the counterclockwise spreading waves, when the fiber coil is at rest.
However, when the fiber coil rotates, some phase difference occurs between the clockwise waves and the counterclockwise waves in proportion to the angular velocity of the fiber coil. The coupler combines the once divided clockwise and counterclockwise waves together. The combined waves pass reversely through the polarizer P and through the first coupler. Then the waves reach a photodetector 113 which converts the light power into an electric signal. Synchronous detection of the output of the photodetector originates a value which is proportional to the phase difference .increment..theta..
The phase of light waves must be modulated. There are some kinds of phase modulators. A phase modulator 114 is constructed by winding a part of the fiber coil around a columnar or cylindrical vibrator having electrodes. Application of alternating voltage upon the electrodes induces vibrations of the piezoelectric column or cylinder. The fiber is subjected to a periodic expansion and shrink. The expansion and contraction of the fiber changes the phase of the light waves passing in the fiber due to the optoelastic effect.
The phase modulator endows periodic changes of phase to the clockwise waves and the counterclockwise waves at different times. Thus the phase changes given by the modulator to the CW waves and CCW waves do not cancel each other at the photodetector. The periodic phase changes survive the interference of the CW and CCW waves at the photodetector.
The output of the photodetector includes a Fundamental component and all harmonies of the modulation frequency. Odd number harmonics contain the phase difference .increment..theta. in the form of sin .increment..theta.. Even number harmonies include the same phase difference .increment..theta. in the form of cos .increment..theta.. The coefficients of the n-th order harmonies are the n-th order Bessel function of .xi., i.e. the phase modulation depth.
The phase modulation method of a fiber-optic gyroscope gives the electric field E.sub.R (t) of the clockwise-propagation waves and E.sub.L (t) of the counterclockwise-propagation waves as follows; EQU E.sub.R (t)=E.sub.R sin {.omega.t=b sin(.omega.t=o/2)+.increment..theta./2}(1) EQU E.sub.L (t)=E.sub.L sin }.omega.t=b sin(.omega.t-o/2) -.increment..theta./2}(2)
where E.sub.R and E.sub.L are amplitudes of the clockwise light waves and the counterclockwise light waves, .OMEGA. is the angular frequency of the phase modulation, .omega. is the angular frequency of the light, .increment..theta. is Sagnac phase difference in proportion to the rotation of the fiber coil. "5426 " is the phase difference induced from the time difference .tau. of passing through the phase-modulator between the clockwise and counterclockwise waves. EQU o=.OMEGA..tau. (3) EQU .tau.=n L/c (4)
Sagnac phase difference is given by EQU .increment..theta.=4.pi.L a.OMEGA.c/(c .lambda.) (5)
Since the phase-modulator is placed at an end of the fiber coil, .tau. is equal to the time for light to pass through the fiber coil. "n" is the refractive index of the core of the fiber, and "L" is the length of the optical fiber of the fiber coil. "c" is the velocity of light in vacuum. .OMEGA. c is the angular velocity of the fiber coil, i.e. the object of the measurement.
The photodetector makes the CW waves and CCW waves interfere with each other and detects the intensity of the interfering Waves by converting the light power into an electric signal. Namely the output of the photodetector is the square of the sum of the CW waves and CCW waves. However, the light frequency .omega. is too high for the photodetector to detect it. Thus, the output of the photodetector gives a time average of the square of the sum regarding .omega.. The output signal I(t) of the photodetector is given by the square of the sum of the electric fields of the CW and CCW waves. EQU I(t)=.vertline.E.sub.R +E.sub.L .vertline..sup.2 (6)
Substituting Eq.(1) and Eq.(2) into Eq.(6), we obtain EQU I(t)=.vertline.(E.sub.R.sup.2 +E.sub.L.sup.2)/2+2E.sub.R E.sub.L sin {.omega.t+b sin (.OMEGA.t+o/2)+.increment..theta./2} sin {.omega.t+b sin (.omega.t-(o/2))-.increment..theta./2}.vertline. (7)
From the product-to-sum formula of sine function and the omission of high frequency vibration of light waves, the output of the photodetector becomes EQU I(t)=(E.sub.R.sup.2 +E.sub.L.sup.2)/2+E.sub.R E.sub.L cos[b{sin (.OMEGA.t+(o/2))-sin (.omega.t-(o/2)) }+.increment..theta.](8)
The sum-to-product formula of sine function changes Eq.(8) to EQU E(t)=(E.sub.R.sup.2 +E.sub.L.sup.2)/2+E.sub.R E.sub.L cos [ }2 b sin(o/2)cos(.OMEGA.t)}+.increment..theta.} (9)
The cosine law transforms Eq.(9) to EQU I(t)=(E.sub.R.sup.2 E.sub.L.sup.2)/2+E.sub.r E.sub.L [cos {2 b sin(o/2)cos(.OMEGA.t)}cos .increment..theta.-sin {2 b sin(o/2)cos(.OMEGA.t)} sin ".theta.] (10)
Bessel functions give a series of expansion of a cosine function and a sine function including variable t in the form of cosine or sine. EQU I(t)=(E.sub.R.sup.2 +E.sub.L.sup.2)/2+E.sub.R E.sub.L [{J.sub.o (.xi.)+2.SIGMA..sub.n-1 (-1).sup.n J.sub.2n (.xi.)cos(2n.OMEGA.t)}cos .increment..theta.-{2.SIGMA..sub.n-o (-1).sup.n J.sub.2n+1 (.xi.)cos(2n+1).OMEGA.t}sin .increment..theta.] (11)
The range of the order number n is from n=1 to n=.infin. or from n=0 to n=.infin. in the summations. Eq.(11) is a Bessel function representation of the output of the detector. The output contains a basic signal and all harmonies of the phase-modulation frequency .OMEGA.. The n-th order harmonies has the n-th order Bessel function J.sub.n (.xi.) as the coefficient. .xi. is a parameter of phase-modulation determined by the amplitude b of phase change and the phase delay o in the fiber coil. EQU .xi.=2b sin(o/2) (12)
Eq.(11) teaches that all harmonies of the modulation frequency are included in the output of the photodetector as a series of Bessel function expansion.
If the output is synchronously detected with a carrier of the frequency of n times as high as the modulation frequency .OMEGA., the n-th harmonies will be obtained.
I Among the components of the photodetector, the basic (fundamental) component I(.OMEGA.,t) with the frequency .OMEGA. is written as EQU I(.OMEGA.,t)=E.sub.R E.sub.L J.sub.1 (.xi.)cos(.OMEGA.t)sin.increment..theta. (13)
The basic component includes .increment..theta.in the form of sin .increment..theta.. Synchronous detection by cos(.OMEGA.t) results in a first order component. EQU I(.OMEGA.,t)=E.sub.R E.sub.L J.sub.1 (.xi.)sin.increment..theta.(14)
The angular velocity of the fiber coil is obtained from the basic component I(.OMEGA.). This is an ordinary way for measuring the angular velocity by the phase-modulation method. Synchronous detection is the most popular technique for the phase-modulation method.
However, the output of the synchronous detection (demodulation) fluctuates according to the variation of the gain of a signal processing circuit and the displacement of optics. Such factors change the basic component I(.xi.) even for the same .increment..theta.. The proportion constant between the basic component and the angular velocity is called a scale factor. The variation of output of the photodetector for the constant rotation is called a fluctuation of the scale factor. Since the scale factor is determined by various parameters, the scale factor fluctuates by many reasons. For example, the changes of gains of electric circuit or the displacement of optical parts induce the fluctuation of the scale factor.
The light amplitude (E.sub.R and E.sub.L) is changed by a misalignment of optics, by a variation of light power at the light source or by a degradation of sensitivity of the photodetector. The amplitude b of the phase modulation is also changed by the temperature dependence of the piezoelectricity of the piezoelectric oscillator. Various reasons cause the fluctuation of the scale factor.
Some improvements have been proposed to solve the difficulty of the fluctuation of the scale factor. 1 Japanese Patent Laying Open No. 60-78314 (78314/'85) 2 Japanese Patent Laying Open No. 60-135816 (135816/'85) 3 Japanese Patent Laying Open No. 61-117410 (117410/'86) 4 Japanese Patent Laying Open No. 61-124817 (124817/'86) 5 Japanese Patent Laying Open No. 61-147106 (147106/'86) 6 Japanese Patent Laying Open No. 63-138208 (138208/'88)
Some calibrate the light power or the phase modulation constant by higher order harmonies of the output of the detector. Others adjust the light power or the phase modulation constant parameters for feeding the fluctuation negatively back to the light source or tile power source of the modulator. These proposals have succeeded in the purpose of suppressing the fluctuation of the scale factor to some extent. Some of them have been put into practice in optical fiber gyroscopes of automobiles. However, these methods incur drawbacks of complexity of signal processing circuits and high cost of production. Calibration or feeding back of the light power or the modulation constant causes a new ground of fluctuation of the light power or the modulation. These improvements require additional devices for reducing the newly brought fluctuation.
Other methods have been proposed so far for deducing the angular velocity by measuring the times of some signals instead of synchronous detection. 7 Japanese Patent Laying Open No. 61-284607 (284607/'86) 8 Japanese Patent laying Open No. 62-80512 (80512/'87) 9 Japanese Patent Laying Open No. 62-212514 (212514/'87) .circle. 10 Japanese Patent Laying Open No. 3-118415 (118415/'91)
Among them, 7 and 9 apply a phase-modulation of triangle waves to the light signal. The triangle waves demand a high speed phase modulation, because a triangle wave is constructed by an assembly of many sine waves of higher frequencies. A cheap piezoelectric oscillator is inappropriate for the phase modulator because of the low speed action of piezoelectricity. 8 and .circle. 10 employ the sine wave modulation. The phase modulator can be composed by a cheap piezoelectric device. However, they are perhaps annoyed with the complexity of the signal processing circuits. 8 divides the output of a photodetector into halves and modulates two partial outputs by two modulation signals with a phase difference of 90 degrees. Although this is a dexterous method, new problems are originated on the signal processing by the phase difference and the amplitude error between two,phase modulation signals. This drawback also plagues .circle. 10 which searches maximum points and minimum points. The performance for a gyroscope is deteriorated by the instability of the additional circuit for searching maximum points and minimum points. Each prior art is annoyed with inherent drawbacks.